Answer: 0.32
Step-by-step explanation:
Answer:
Step-by-step explanation:
Total number of pairs of socks in a drawer = 10
Number of black pairs of socks = 5
Number of blue pairs of socks = 5
A. If you picked 2 socks [black] and [blue] 3rd pick guarantees you will have one pair of either blue or black
Number of socks you pull out to guarantee that you have a pair of one color = 3 socks
B. If you want to pick 2 good pairs and your 6 picks are worst case, so 7th pick of the socks will give you good pair of two colors.
Number of socks you pull out to have two good pairs = 7 socks
C. If you want to have a pair of black socks your worst case will be you pick all 10 blue socks so another 2 socks must be black.
Number of socks you pull out to have two black socks = 12 socks
Answer:
84%
Step-by-step explanation:
The probability of Thomas bumping into her at school is 80%, so the probability of not bumping into her is 100% - 80% = 20%.
If he doesn't bump into her (20% chance), he will call her, and the probability of asking her in this case is 60%, so the final probability of asking her in this case is:
![P_1 = 20\% * 60\% = 12\%](https://tex.z-dn.net/?f=P_1%20%3D%2020%5C%25%20%2A%2060%5C%25%20%3D%2012%5C%25)
If he bumps into her (80% chance), the probability of asking her is 90%, so the final probability of asking her in this case is:
![P_2 = 80\% * 90\% = 72\%](https://tex.z-dn.net/?f=P_2%20%3D%2080%5C%25%20%2A%2090%5C%25%20%3D%2072%5C%25)
To find the probability of Thomas inviting Madeline to the party, we just have to sum the probabilities we found above:
![P = P_1 + P_2](https://tex.z-dn.net/?f=P%20%3D%20P_1%20%2B%20P_2)
![P = 12\% + 72\% = 84\%](https://tex.z-dn.net/?f=P%20%3D%2012%5C%25%20%2B%2072%5C%25%20%3D%2084%5C%25)
Yes, the partition gives the two brothers equal shares.
Step-by-step explanation:
Step 1:
Assume the entire field has an area of B. So one brother takes
,
, and
So we need to calculate how much this brother takes in terms of B.
To do this we calculate how much
is.
Step 2:
To add
,
First take the LCM of the denominators 12, 6, and 4
The LCM is 12, we multiply the denominator to get the LCM value, this same value is multiplied to the numerator too.
![\frac{1}{12} B + \frac{1}{6} B + \frac{1}{4} B = \frac{1(1)}{12(1)} B + \frac{1(2)}{6(2)} B + \frac{1(3)}{4(3)} B \\\\\frac{1}{12} B + \frac{1}{6} B + \frac{1}{4} B= \frac{1B +2B+3B}{12} = \frac{B}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B12%7D%20B%20%2B%20%5Cfrac%7B1%7D%7B6%7D%20B%20%2B%20%5Cfrac%7B1%7D%7B4%7D%20B%20%3D%20%5Cfrac%7B1%281%29%7D%7B12%281%29%7D%20B%20%2B%20%5Cfrac%7B1%282%29%7D%7B6%282%29%7D%20B%20%2B%20%5Cfrac%7B1%283%29%7D%7B4%283%29%7D%20B%20%5C%5C%5C%5C%5Cfrac%7B1%7D%7B12%7D%20B%20%2B%20%5Cfrac%7B1%7D%7B6%7D%20B%20%2B%20%5Cfrac%7B1%7D%7B4%7D%20B%3D%20%5Cfrac%7B1B%20%2B2B%2B3B%7D%7B12%7D%20%3D%20%5Cfrac%7BB%7D%7B2%7D)
Step 3:
One brother gets
, so we need to calculate how much the other brother gets.
The other brother's share = ![B - \frac{1}{2} B = \frac{1}{2}B](https://tex.z-dn.net/?f=B%20-%20%5Cfrac%7B1%7D%7B2%7D%20B%20%3D%20%5Cfrac%7B1%7D%7B2%7DB)
So both the brothers get equal shares